Journal of Lie Theory

no. 2
Orbital Reducibility and a Generalization of Lambda Symmetries
Journal of Lie Theory, Volume 23 (2013) no. 2, pp. 357-381
We review the notion of reducibility and we introduce and discuss the notion of orbital reducibility for autonomous ordinary differential equations of first order. The relation between (orbital) reducibility and (orbital) symmetry is investigated and employed to construct (orbitally) reducible systems. By standard identifications, the notions extend to non-autonomous ODEs of first and higher order. Moreover we thus obtain a generalization of the lambda symmetries of Muriel and Romero. Several examples are given.
DOI: 10.5802/jolt.729
Classification: 34A05, 34C14, 34A25, 34A26
Keywords: Symmetry, reduction, vector field 
@article{JOLT_2013_23_2_a1,
     author = {G. Cicogna and G. Gaeta and S. Walcher},
     title = {Orbital {Reducibility} and a {Generalization} of {Lambda} {Symmetries}},
     journal = {Journal of Lie Theory},
     pages = {357--381},
     year = {2013},
     volume = {23},
     number = {2},
     doi = {10.5802/jolt.729},
     zbl = {1286.34056},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.729/}
}
TY  - JOUR
AU  - G. Cicogna
AU  - G. Gaeta
AU  - S. Walcher
TI  - Orbital Reducibility and a Generalization of Lambda Symmetries
JO  - Journal of Lie Theory
PY  - 2013
SP  - 357
EP  - 381
VL  - 23
IS  - 2
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.729/
DO  - 10.5802/jolt.729
ID  - JOLT_2013_23_2_a1
ER  - 
%0 Journal Article
%A G. Cicogna
%A G. Gaeta
%A S. Walcher
%T Orbital Reducibility and a Generalization of Lambda Symmetries
%J Journal of Lie Theory
%D 2013
%P 357-381
%V 23
%N 2
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.729/
%R 10.5802/jolt.729
%F JOLT_2013_23_2_a1
G. Cicogna; G. Gaeta; S. Walcher. Orbital Reducibility and a Generalization of Lambda Symmetries. Journal of Lie Theory, Volume 23 (2013) no. 2, pp. 357-381. doi: 10.5802/jolt.729

Cited by Sources: